Finite Group Databasebeta

← C37×#61977 #22683230

Subgroups — C37×#61977 #22683230

Order 9472.

1980 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3508C211yesmaximal, characteristic, complemented
2C37×#3481C211yesmaximal, characteristic, complemented
3C37×#3403C212yesmaximal, complemented
4C37×#3370C212yesmaximal, complemented
5C37×#3314C212yesmaximal, complemented
6C37×#3309C212yesmaximal, complemented
7C37×#3297C212yesmaximal, complemented
8C37×#3280C212yesmaximal, complemented
9C37×#3268C212yesmaximal, complemented
10C37×#3264C212yesmaximal, complemented
11C37×#3251C211yesmaximal, characteristic, complemented
12C37×#3248C211yesmaximal, characteristic, complemented
13C37×#3245C211yesmaximal, characteristic, complemented
14C37×#3217C211yesmaximal, characteristic, complemented
15C37×#3214C211yesmaximal, characteristic, complemented
16C37×#3212C211yesmaximal, characteristic, complemented
17C37×#3115C211yesmaximal, characteristic, complemented
18C37×#3110C211yesmaximal, characteristic, complemented
19C37×#3100C211yesmaximal, characteristic, complemented
20C37×#3036C211yesmaximal, characteristic, complemented
21C37×#3035C211yesmaximal, characteristic, complemented
22C2×C37×#459C211yesmaximal, characteristic, complemented
23C37×#2990C211yesmaximal, characteristic, complemented
24C2×AGL(1,ℤ/8)×C37C2212yescomplemented
25C2×#135×C37C2212yescomplemented
26C22×D8×C37C2212yes—
27C37×#559—21no—
28C37×#559C2211yescharacteristic, complemented
29C37×#559C2212yescomplemented
30C37×#554C2211yescharacteristic
31C37×#554C2211yescharacteristic, complemented
32C37×#553—21no—
33C37×#553C2211yescharacteristic
34C37×#553C2211yescharacteristic, complemented
35C37×#551—21no—
36C37×#551—21no—
37C37×#550—21no—
38C37×#550C2212yescomplemented
39C37×#546—21no—
40C37×#546—21no—
41C37×#546—21no—
42C37×#546C2211yescharacteristic
43C37×#546C2212yes—
44C37×#546C2211yescharacteristic, complemented
45C37×#546C2212yescomplemented
46D42×C37C2211yescharacteristic
47C37×#540—21no—
48C37×#540—21no—
49C37×#535—21no—
50C37×#533C2211yescharacteristic, complemented
51C37×#532C2211yescharacteristic, complemented
52C37×#532C2211yescharacteristic, complemented
53C37×#532C2211yescharacteristic, complemented
54C37×#532C2211yescharacteristic, complemented
55C37×#532C2211yescharacteristic, complemented
56C2×#127×C37C2211yescharacteristic, complemented
57C37×#529—21no—
58C37×#529C2211yescharacteristic
59C37×#529C2211yescharacteristic, complemented
60C37×#525—21no—
61C37×#525—21no—
62C37×#518—21no—
63C4×#41×C37C2211yescharacteristic
64C4×#41×C37C2211yescharacteristic, complemented
65C2×C4×D4×C37—21no—
66C2×C4×D4×C37C2211yescharacteristic
67C2×C4×D4×C37C2211yescharacteristic, complemented
68C37×#496C2212yescomplemented
69C37×#496C2212yescomplemented
70C37×#495C2212yescomplemented
71C37×#490C2212yescomplemented
72C37×#489C2212yescomplemented
73C37×#488C2212yescomplemented
74C37×#484C2212yescomplemented
75C37×#482C2212yescomplemented
76C37×#480C2212yescomplemented
77C37×#479C2212yescomplemented
78C37×#478C2212yescomplemented
79C37×#475C2211yescharacteristic, complemented
80C37×#474C2211yescharacteristic, complemented
81C37×#474C2211yescharacteristic, complemented
82C37×#474C2212yescomplemented
83C37×#474C2211yescharacteristic, complemented
84C37×#469C2212yescomplemented
85C37×#468C2212yescomplemented
86C37×#467C2212yescomplemented
87C37×#466C2212yescomplemented
88C37×#466C2212yescomplemented
89C37×#465C2212yes—
90C37×#464C2212yescomplemented
91C37×#464C2212yescomplemented
92C37×#463C2212yescomplemented
93C37×#463C2212yescomplemented
94C37×#463C2212yescomplemented
95C37×#463C2212yescomplemented
96C37×#462C2211yescharacteristic, complemented
97C37×#461C2211yescharacteristic, complemented
98C37×#461C2211yescharacteristic, complemented
99C37×#461C2211yescharacteristic, complemented
100C37×#460C2211yescharacteristic, complemented
101C37×#460C2211yescharacteristic, complemented
102C37×#459C2212yes—
103C37×#459C2211yescharacteristic
104C37×#459C2211yescharacteristic
105C37×#459C2212yescomplemented
106C37×#459C2212yescomplemented
107C37×#459C2211yescharacteristic, complemented
108C37×#459C2211yescharacteristic, complemented
109C37×#459C2211yescharacteristic, complemented
110C37×#459C2211yescharacteristic, complemented
111C37×#452C2212yescomplemented
112C37×#450C2212yes—
113C37×#450C2212yescomplemented
114C37×#449C2212yescomplemented
115C37×#449C2212yescomplemented
116C37×#449C2212yescomplemented
117C37×#449C2212yescomplemented
118C37×#447C2212yes—
119C37×#447C2212yescomplemented
120C37×#446C2212yescomplemented
121C37×#442C2212yescomplemented
122C37×#440C2212yescomplemented
123C37×#440C2212yescomplemented
124C37×#440C2212yescomplemented
125C4×D8×C37C2212yescomplemented
126C4×D8×C37C2212yescomplemented
127C37×#435C2212yes—
128C37×#435C2212yescomplemented
129C8×D4×C37C2212yescomplemented
130C37×#432C2211yescharacteristic, complemented
131C37×#432C2211yescharacteristic, complemented
132C37×#431C2211yescharacteristic, complemented
133C37×#423C2211yescharacteristic, complemented
134C2×C4⋊C8×C37C2211yescharacteristic, complemented
135C2×C4⋊C8×C37C2211yescharacteristic, complemented
136C37×#417C2212yescomplemented
137C37×#416C2212yescomplemented
138C2×#102×C37C2212yescomplemented
139C2×#41×C37—21no—
140C2×#41×C37—21no—
141C2×#41×C37—21no—
142C2×#41×C37D411yescharacteristic
143C2×#41×C37C2311yescharacteristic
144C2×#41×C37C2312yes—
145C2×#41×C37C2312yes—
146C22×D4×C37—21no—
147C22×D4×C37—21no—
148C22×D4×C37—21no—
149C22×D4×C37C2311yescharacteristic
150C22×D4×C37C2311yescharacteristic
151C22×D4×C37C2312yes—
152C23×C4×C37—21no—
153C23×C4×C37—21no—
154AGL(1,ℤ/8)×C37—44no—
155#135×C37—44no—
156C2×Q16×C37C2312yes—
157C2×SD16×C37C2312yes—
158C2×SD16×C37C2312yes—
159C2×SD16×C37C2312yes—
160C2×SD16×C37C2312yes—
161C2×SD16×C37C2312yes—
162C2×D8×C37—44no—
163C2×D8×C37C2312yes—
164C2×D8×C37C2312yes—
165C2×D8×C37C2312yes—
166C2×D8×C37C2312yes—
167C2×D8×C37C2312yes—
168C2×D8×C37C2312yes—
169C2×M16×C37C2312yes—
170C22×C8×C37C2312yes—
171C22×C8×C37C2312yes—
172C4⋊Q8×C37C2311yescharacteristic
173C4⋊Q8×C37C2311yescharacteristic
174C4⋊Q8×C37C2311yescharacteristic
175#127×C37—22no—
176#127×C37—21no—
177#127×C37—21no—
178#127×C37C2311yescharacteristic
179#127×C37C2311yescharacteristic
180#127×C37C2312yes—
181#127×C37C2311yescharacteristic
182#126×C37—21no—
183#126×C37—21no—
184#126×C37—21no—
185#126×C37—21no—
186#125×C37—21no—
187#125×C37—21no—
188#125×C37C2311yescharacteristic
189#125×C37C2311yescharacteristic
190#124×C37—21no—
191#124×C37—22no—
192#124×C37—21no—
193#124×C37—21no—
194#124×C37—21no—
195#124×C37C2311yescharacteristic
196#124×C37C2311yescharacteristic
197#124×C37C2312yes—
198#124×C37C2312yes—
199#123×C37—21no—
200#123×C37—21no—
201#123×C37—21no—
202#123×C37—21no—
203#123×C37—21no—
204#123×C37—21no—
205#123×C37—22no—
206#123×C37—22no—
207#123×C37—22no—
208#123×C37—22no—
209#123×C37—21no—
210#123×C37—21no—
211C22⋊Q8×C37—21no—
212C22⋊Q8×C37—21no—
213C22⋊Q8×C37—21no—
214C22⋊Q8×C37—21no—
215C22⋊Q8×C37—21no—
216C22⋊Q8×C37—21no—
217C22⋊Q8×C37C2311yescharacteristic
218C22⋊Q8×C37C2311yescharacteristic
219C22⋊Q8×C37C2312yes—
220#121×C37—21no—
221#121×C37—21no—
222#121×C37—21no—
223#121×C37—21no—
224#121×C37—21no—
225#121×C37—21no—
226#121×C37—21no—
227#121×C37—21no—
228#121×C37—21no—
229#121×C37—21no—
230#121×C37—21no—
231#121×C37—21no—
232#121×C37—22no—
233#121×C37—22no—
234#121×C37—22no—
235#121×C37—22no—
236#121×C37C2311yescharacteristic
237#121×C37C2311yescharacteristic
238#121×C37C2312yes—
239#121×C37C2311yescharacteristic
240#121×C37C2312yes—
241#121×C37C2311yescharacteristic
242#120×C37—21no—
243#120×C37—21no—
244#120×C37—22no—
245#120×C37—22no—
246#120×C37—21no—
247#120×C37—21no—
248C4×Q8×C37—21no—
249C4×Q8×C37D411yescharacteristic
250C4×Q8×C37C2311yescharacteristic
251C4×Q8×C37C2312yes—
252C4×Q8×C37C2311yescharacteristic
253C4×Q8×C37C2311yescharacteristic
254C4×D4×C37—21no—
255C4×D4×C37—21no—
256C4×D4×C37—21no—
257C4×D4×C37—21no—
258C4×D4×C37—21no—
259C4×D4×C37—22no—
260C4×D4×C37—22no—
261C4×D4×C37—21no—
262C4×D4×C37—21no—
263C4×D4×C37—21no—
264C4×D4×C37—21no—
265C4×D4×C37—21no—
266C4×D4×C37—21no—
267C4×D4×C37—21no—
268C4×D4×C37—21no—
269C4×D4×C37—21no—
270C4×D4×C37—21no—
271C4×D4×C37—21no—
272C4×D4×C37—21no—
273C4×D4×C37—21no—
274C4×D4×C37—21no—
275C4×D4×C37D411yescharacteristic
276C4×D4×C37D411yescharacteristic
277C4×D4×C37D411yescharacteristic
278C4×D4×C37C2311yescharacteristic
279C4×D4×C37C2311yescharacteristic
280C4×D4×C37C2312yes—
281C4×D4×C37C2312yes—
282C4×D4×C37C2311yescharacteristic
283C4×D4×C37C2311yescharacteristic
284C4×D4×C37C2311yescharacteristic
285C4×D4×C37C2311yescharacteristic
286C4×D4×C37C2311yescharacteristic
287C4×D4×C37C2311yescharacteristic
288C4×D4×C37C2311yescharacteristic
289C4×D4×C37C2311yescharacteristic
290C4×D4×C37C2311yescharacteristic
291#117×C37—21no—
292#117×C37—21no—
293#117×C37—21no—
294#117×C37—21no—
295#117×C37D411yescharacteristic
296#117×C37D411yescharacteristic
297#117×C37D411yescharacteristic
298#117×C37C2311yescharacteristic
299C2×C4⋊C4×C37—21no—
300C2×C4⋊C4×C37C2311yescharacteristic
301C2×C4⋊C4×C37C2311yescharacteristic
302C2×C22⋊C4×C37—21no—
303C2×C22⋊C4×C37—21no—
304C2×C22⋊C4×C37—22no—
305C2×C22⋊C4×C37—22no—
306C2×C22⋊C4×C37—21no—
307C2×C22⋊C4×C37—21no—
308C2×C42×C37—21no—
309C2×C42×C37C2311yescharacteristic
310C2×C42×C37C2311yescharacteristic
311C2×C42×C37C2311yescharacteristic
312#107×C37C2312yes—
313#107×C37C2312yes—
314#107×C37C2312yes—
315#106×C37C2312yes—
316C4⋊C8×C37C2311yescharacteristic
317C4⋊C8×C37C2311yescharacteristic
318C4⋊C8×C37C2311yescharacteristic
319C4⋊C8×C37C2312yes—
320C4⋊C8×C37C2312yes—
321C4⋊C8×C37C2312yes—
322C4⋊C8×C37C2311yescharacteristic
323#103×C37C2312yes—
324#103×C37C2312yes—
325#103×C37C2312yes—
326#103×C37C2312yes—
327#103×C37C2312yes—
328#102×C37C2312yes—
329#102×C37C2312yes—
330#102×C37C2312yes—
331#102×C37C2312yes—
332#102×C37C2312yes—
333#102×C37C2312yes—
334#102×C37C2312yes—
335#102×C37C2312yes—
336#102×C37C2312yes—
337#102×C37C2312yes—
338#102×C37C2312yes—
339C22⋊C8×C37C2312yes—
340C22⋊C8×C37C2312yes—
341C22⋊C8×C37C2312yes—
342#97×C37C2312yes—
343#97×C37C2312yes—
344C4×C8×C37C2312yes—
345C24×C37—21no—
346C24×C37—21no—
347C24×C37—22no—
348#41×C37—22no—
349#41×C37—42no—
350#41×C37—41no—
351#41×C37—42no—
352#41×C37—42no—
353#41×C37—42no—
354#41×C37—42no—
355#41×C37—82no—
356#41×C37—82no—
357#41×C37—82no—
358C2×Q8×C37—21no—
359C2×Q8×C37—21no—
360C2×Q8×C37C2×D411yescharacteristic
361C2×Q8×C37C2412yes—
362C2×Q8×C37C2411yescharacteristic
363C2×D4×C37—22no—
364C2×D4×C37—22no—
365C2×D4×C37—21no—
366C2×D4×C37—21no—
367C2×D4×C37—21no—
368C2×D4×C37—22no—
369C2×D4×C37—22no—
370C2×D4×C37—21no—
371C2×D4×C37—21no—
372C2×D4×C37—22no—
373C2×D4×C37—22no—
374C2×D4×C37—21no—
375C2×D4×C37—21no—
376C2×D4×C37—21no—
377C2×D4×C37—21no—
378C2×D4×C37—21no—
379C2×D4×C37—22no—
380C2×D4×C37—21no—
381C2×D4×C37—21no—
382C2×D4×C37—21no—
383C2×D4×C37—22no—
384C2×D4×C37—22no—
385C2×D4×C37—41no—
386C2×D4×C37—41no—
387C2×D4×C37—42no—
388C2×D4×C37—42no—
389C2×D4×C37—44no—
390C2×D4×C37—44no—
391C2×D4×C37—82no—
392C2×D4×C37C2×D411yescharacteristic
393C2×D4×C37C2×D411yescharacteristic
394C2×D4×C37C2×D411yescharacteristic
395C2×D4×C37C2412yes—
396C2×D4×C37C2412yes—
397C2×D4×C37C2411yescharacteristic
398C2×D4×C37C2411yescharacteristic
399C2×D4×C37C2411yescharacteristic
400C22×C4×C37—21no—
401C22×C4×C37—21no—
402C22×C4×C37—21no—
403C22×C4×C37—21no—
404C22×C4×C37—21no—
405C22×C4×C37—21no—
406C22×C4×C37—21no—
407C22×C4×C37—21no—
408C22×C4×C37—21no—
409C22×C4×C37—22no—
410C22×C4×C37—22no—
411C22×C4×C37—22no—
412C22×C4×C37—22no—
413C22×C4×C37—21no—
414C22×C4×C37—21no—
415C22×C4×C37—82no—
416C22×C4×C37—82no—
417C22×C4×C37C2×D411yescharacteristic
418C22×C4×C37C2×D411yescharacteristic
419C22×C4×C37C2×D411yescharacteristic
420C22×C4×C37C2×D411yescharacteristic
421C22×C4×C37C2×D411yescharacteristic
422C22×C4×C37C2×D411yescharacteristic
423C22×C4×C37C2411yescharacteristic
424C22×C4×C37C2411yescharacteristic
425C22×C4×C37C2411yescharacteristic
426Q16×C37—42no—
427SD16×C37—24no—
428SD16×C37—42no—
429SD16×C37—42no—
430SD16×C37—42no—
431SD16×C37—42no—
432D8×C37—24no—
433D8×C37—24no—
434D8×C37—42no—
435D8×C37—42no—
436D8×C37—42no—
437D8×C37—42no—
438M16×C37—42no—
439C2×C8×C37—42no—
440C2×C8×C37—42no—
441C2×C8×C37C2412yes—
442C2×C8×C37C2412yes—
443C2×C8×C37C2412yes—
444C2×C8×C37C2412yes—
445C4⋊C4×C37—21no—
446C4⋊C4×C37—21no—
447C4⋊C4×C37—21no—
448C4⋊C4×C37—21no—
449C4⋊C4×C37—21no—
450C4⋊C4×C37—21no—
451C4⋊C4×C37—21no—
452C4⋊C4×C37—21no—
453C4⋊C4×C37—21no—
454C4⋊C4×C37—21no—
455C4⋊C4×C37—21no—
456C4⋊C4×C37—21no—
457C4⋊C4×C37—21no—
458C4⋊C4×C37—21no—
459C4⋊C4×C37—22no—
460C4⋊C4×C37—22no—
461C4⋊C4×C37C2×D411yescharacteristic
462C4⋊C4×C37C2×D411yescharacteristic
463C4⋊C4×C37C2×D411yescharacteristic
464C4⋊C4×C37C2×D411yescharacteristic
465C4⋊C4×C37C2×D411yescharacteristic
466C4⋊C4×C37C2×D411yescharacteristic
467C4⋊C4×C37C2411yescharacteristic
468C4⋊C4×C37C2411yescharacteristic
469C4⋊C4×C37C2411yescharacteristic
470C4⋊C4×C37C2411yescharacteristic
471C4⋊C4×C37C2412yes—
472C22⋊C4×C37—22no—
473C22⋊C4×C37—21no—
474C22⋊C4×C37—21no—
475C22⋊C4×C37—21no—
476C22⋊C4×C37—21no—
477C22⋊C4×C37—22no—
478C22⋊C4×C37—22no—
479C22⋊C4×C37—22no—
480C22⋊C4×C37—22no—
481C22⋊C4×C37—21no—
482C22⋊C4×C37—21no—
483C22⋊C4×C37—21no—
484C22⋊C4×C37—21no—
485C22⋊C4×C37—21no—
486C22⋊C4×C37—21no—
487C22⋊C4×C37—21no—
488C22⋊C4×C37—21no—
489C22⋊C4×C37—21no—
490C22⋊C4×C37—21no—
491C22⋊C4×C37—21no—
492C22⋊C4×C37—21no—
493C22⋊C4×C37—21no—
494C22⋊C4×C37—21no—
495C22⋊C4×C37—21no—
496C22⋊C4×C37—22no—
497C22⋊C4×C37—22no—
498C22⋊C4×C37—22no—
499C22⋊C4×C37—22no—
500C22⋊C4×C37C2×D411yescharacteristic
501C22⋊C4×C37C2×D411yescharacteristic
502C22⋊C4×C37C2×D411yescharacteristic
503C22⋊C4×C37C2×D411yescharacteristic
504C22⋊C4×C37C2×D411yescharacteristic
505C22⋊C4×C37C2×D411yescharacteristic
506C42×C37—21no—
507C42×C37—21no—
508C42×C37—21no—
509C42×C37—22no—
510C42×C37C2×D411yescharacteristic
511C42×C37C2×D411yescharacteristic
512C42×C37C2×D411yescharacteristic
513C42×C37C2×D411yescharacteristic
514C42×C37C2×D411yescharacteristic
515C42×C37C2×D411yescharacteristic
516C42×C37C2411yescharacteristic
517C42×C37C2411yescharacteristic
518C42×C37C2411yescharacteristic
519C42×C37C2411yescharacteristic
520C23×C37—21no—
521C23×C37—21no—
522C23×C37—21no—
523C23×C37—22no—
524C23×C37—22no—
525C23×C37—42no—
526C23×C37—42no—
527C23×C37—42no—
528C23×C37—42no—
529C23×C37—44no—
530C23×C37—81no—
531C23×C37—81no—
532C23×C37—82no—
533C23×C37—82no—
534C23×C37C22×D411yescharacteristic
535C23×C37C22×D411yescharacteristic
536C23×C37C22×D411yescharacteristic
537Q8×C37—22no—
538Q8×C37—21no—
539Q8×C37—21no—
540Q8×C37—22no—
541Q8×C37—41no—
542Q8×C37—42no—
543Q8×C37—81no—
544D4×C37—22no—
545D4×C37—22no—
546D4×C37—22no—
547D4×C37—22no—
548D4×C37—21no—
549D4×C37—21no—
550D4×C37—21no—
551D4×C37—21no—
552D4×C37—22no—
553D4×C37—21no—
554D4×C37—22no—
555D4×C37—41no—
556D4×C37—42no—
557D4×C37—42no—
558D4×C37—42no—
559D4×C37—42no—
560D4×C37—44no—
561D4×C37—42no—
562D4×C37—42no—
563D4×C37—42no—
564D4×C37—42no—
565D4×C37—42no—
566D4×C37—42no—
567D4×C37—82no—
568D4×C37—82no—
569D4×C37—81no—
570D4×C37—82no—
571D4×C37—82no—
572D4×C37—81no—
573D4×C37—81no—
574D4×C37—82no—
575D4×C37—82no—
576D4×C37H(5,𝔽2)12yes—
577C2×C4×C37—22no—
578C2×C4×C37—22no—
579C2×C4×C37—22no—
580C2×C4×C37—22no—
581C2×C4×C37—21no—
582C2×C4×C37—21no—
583C2×C4×C37—21no—
584C2×C4×C37—21no—
585C2×C4×C37—21no—
586C2×C4×C37—21no—
587C2×C4×C37—21no—
588C2×C4×C37—21no—
589C2×C4×C37—21no—
590C2×C4×C37—22no—
591C2×C4×C37—22no—
592C2×C4×C37—21no—
593C2×C4×C37—21no—
594C2×C4×C37—41no—
595C2×C4×C37—41no—
596C2×C4×C37—42no—
597C2×C4×C37—42no—
598C2×C4×C37—42no—
599C2×C4×C37—42no—
600C2×C4×C37—42no—
601C2×C4×C37—81no—
602C2×C4×C37—81no—
603C2×C4×C37—81no—
604C2×C4×C37—81no—
605C2×C4×C37—82no—
606C2×C4×C37—82no—
607C2×C4×C37—82no—
608C2×C4×C37—82no—
609C2×C4×C37—81no—
610C2×C4×C37—81no—
611C2×C4×C37C22×D411yescharacteristic
612C2×C4×C37C22×D411yescharacteristic
613C2×C4×C37C22×D411yescharacteristic
614C2×C4×C37C22×D411yescharacteristic
615C2×C4×C37C22×D411yescharacteristic
616C2×C4×C37C22×D411yescharacteristic
617C2×C4×C37C22×D411yescharacteristic
618C2×C4×C37C22×D411yescharacteristic
619C2×C4×C37C22×D411yescharacteristic
620C2×C4×C37C22×D411yescharacteristic
621C2×C4×C37C22×D411yescharacteristic
622C2×C4×C37C2511yescharacteristic
623C8×C37—22no—
624C8×C37—22no—
625C8×C37—22no—
626C8×C37—22no—
627#61977C3711yesmaximal, characteristic, direct product factor, Sylow
628C22×C37—21no—
629C22×C37—21no—
630C22×C37—21no—
631C22×C37—21no—
632C22×C37—22no—
633C22×C37—21no—
634C22×C37—21no—
635C22×C37—21no—
636C22×C37—21no—
637C22×C37—41no—
638C22×C37—41no—
639C22×C37—42no—
640C22×C37—42no—
641C22×C37—41no—
642C22×C37—41no—
643C22×C37—41no—
644C22×C37—41no—
645C22×C37—42no—
646C22×C37—42no—
647C22×C37—41no—
648C22×C37—41no—
649C22×C37—42no—
650C22×C37—42no—
651C22×C37—84no—
652C22×C37—84no—
653C22×C37—164no—
654C22×C37#57512yes—
655C22×C37C23×D411yescharacteristic
656C4×C37—21no—
657C4×C37—21no—
658C4×C37—21no—
659C4×C37—21no—
660C4×C37—21no—
661C4×C37—21no—
662C4×C37—21no—
663C4×C37—21no—
664C4×C37—21no—
665C4×C37—21no—
666C4×C37—41no—
667C4×C37—42no—
668C4×C37—41no—
669C4×C37—41no—
670C4×C37—41no—
671C4×C37—41no—
672C4×C37—42no—
673C4×C37#57612yes—
674C4×C37C2×H(5,𝔽2)11yescharacteristic
675C4×C37#58511yescharacteristic
676#3508C2×C3711yescharacteristic, complemented
677#3481C2×C3711yescharacteristic, complemented
678#3403C2×C3712yescomplemented
679#3370C2×C3712yescomplemented
680#3314C2×C3712yescomplemented
681#3309C2×C3712yescomplemented
682#3297C2×C3712yescomplemented
683#3280C2×C3712yescomplemented
684#3268C2×C3712yescomplemented
685#3264C2×C3712yescomplemented
686#3251C2×C3711yescharacteristic, complemented
687#3248C2×C3711yescharacteristic, complemented
688#3245C2×C3711yescharacteristic, complemented
689#3217C2×C3711yescharacteristic, complemented
690#3214C2×C3711yescharacteristic, complemented
691#3212C2×C3711yescharacteristic, complemented
692#3115C2×C3711yescharacteristic, complemented
693#3110C2×C3711yescharacteristic, complemented
694#3100C2×C3711yescharacteristic, complemented
695#3036C2×C3711yescharacteristic, complemented
696#3035C2×C3711yescharacteristic, complemented
697C2×#459C2×C3711yescharacteristic, complemented
698#2990C2×C3711yescharacteristic, complemented
699C2×C37—22no—
700C2×C37—41no—
701C2×C37—41no—
702C2×C37—42no—
703C2×C37—81no—
704C2×C37—81no—
705C2×C37—82no—
706C2×C37—82no—
707C2×C37#348811yescharacteristic
708C2×C37C2×#57511yescharacteristic
709C2×C37C2×#57611yescharacteristic
710C2×AGL(1,ℤ/8)C22×C3712yescomplemented
711C2×#135C22×C3712yescomplemented
712C22×D8C22×C3712yes—
713#559—21no—
714#559C22×C3712yescomplemented
715#559C22×C3711yescharacteristic, complemented
716#554C22×C3711yescharacteristic
717#554C22×C3711yescharacteristic, complemented
718#553—21no—
719#553C22×C3711yescharacteristic
720#553C22×C3711yescharacteristic, complemented
721#551—21no—
722#551—21no—
723#550—21no—
724#550C22×C3712yescomplemented
725#546—21no—
726#546—21no—
727#546—21no—
728#546C22×C3711yescharacteristic
729#546C22×C3712yes—
730#546C22×C3711yescharacteristic, complemented
731#546C22×C3712yescomplemented
732D42C22×C3711yescharacteristic
733#540—21no—
734#540—21no—
735#535—21no—
736#533C22×C3711yescharacteristic, complemented
737#532C22×C3711yescharacteristic, complemented
738#532C22×C3711yescharacteristic, complemented
739#532C22×C3711yescharacteristic, complemented
740#532C22×C3711yescharacteristic, complemented
741#532C22×C3711yescharacteristic, complemented
742C2×#127C22×C3711yescharacteristic, complemented
743#529—21no—
744#529C22×C3711yescharacteristic
745#529C22×C3711yescharacteristic, complemented
746#525—21no—
747#525—21no—
748#518—21no—
749C4×#41C22×C3711yescharacteristic
750C4×#41C22×C3711yescharacteristic, complemented
751C2×C4×D4—21no—
752C2×C4×D4C22×C3711yescharacteristic
753C2×C4×D4C22×C3711yescharacteristic, complemented
754#496C22×C3712yescomplemented
755#496C22×C3712yescomplemented
756#495C22×C3712yescomplemented
757#490C22×C3712yescomplemented
758#489C22×C3712yescomplemented
759#488C22×C3712yescomplemented
760#484C22×C3712yescomplemented
761#482C22×C3712yescomplemented
762#480C22×C3712yescomplemented
763#479C22×C3712yescomplemented
764#478C22×C3712yescomplemented
765#475C22×C3711yescharacteristic, complemented
766#474C22×C3711yescharacteristic, complemented
767#474C22×C3711yescharacteristic, complemented
768#474C22×C3711yescharacteristic, complemented
769#474C22×C3712yescomplemented
770#469C22×C3712yescomplemented
771#468C22×C3712yescomplemented
772#467C22×C3712yescomplemented
773#466C22×C3712yescomplemented
774#466C22×C3712yescomplemented
775#465C22×C3712yes—
776#464C22×C3712yescomplemented
777#464C22×C3712yescomplemented
778#463C22×C3712yescomplemented
779#463C22×C3712yescomplemented
780#463C22×C3712yescomplemented
781#463C22×C3712yescomplemented
782#462C22×C3711yescharacteristic, complemented
783#461C22×C3711yescharacteristic, complemented
784#461C22×C3711yescharacteristic, complemented
785#461C22×C3711yescharacteristic, complemented
786#460C22×C3711yescharacteristic, complemented
787#460C22×C3711yescharacteristic, complemented
788#459C22×C3711yescharacteristic
789#459C22×C3712yes—
790#459C22×C3711yescharacteristic
791#459C22×C3711yescharacteristic, complemented
792#459C22×C3712yescomplemented
793#459C22×C3712yescomplemented
794#459C22×C3711yescharacteristic, complemented
795#459C22×C3711yescharacteristic, complemented
796#459C22×C3711yescharacteristic, complemented
797#452C22×C3712yescomplemented
798#450C22×C3712yes—
799#450C22×C3712yescomplemented
800#449C22×C3712yescomplemented
801#449C22×C3712yescomplemented
802#449C22×C3712yescomplemented
803#449C22×C3712yescomplemented
804#447C22×C3712yes—
805#447C22×C3712yescomplemented
806#446C22×C3712yescomplemented
807#442C22×C3712yescomplemented
808#440C22×C3712yescomplemented
809#440C22×C3712yescomplemented
810#440C22×C3712yescomplemented
811C4×D8C22×C3712yescomplemented
812C4×D8C22×C3712yescomplemented
813#435C22×C3712yes—
814#435C22×C3712yescomplemented
815C8×D4C22×C3712yescomplemented
816#432C22×C3711yescharacteristic, complemented
817#432C22×C3711yescharacteristic, complemented
818#431C22×C3711yescharacteristic, complemented
819#423C22×C3711yescharacteristic, complemented
820C2×C4⋊C8C22×C3711yescharacteristic, complemented
821C2×C4⋊C8C22×C3711yescharacteristic, complemented
822#417C22×C3712yescomplemented
823#416C22×C3712yescomplemented
824C2×#102C22×C3712yescomplemented
825C37#6197711yescharacteristic, direct product factor, Sylow
826C2×#41—21no—
827C2×#41—21no—
828C2×#41—21no—
829C2×#41D4×C3711yescharacteristic
830C2×#41C23×C3711yescharacteristic
831C2×#41C23×C3712yes—
832C2×#41C23×C3712yes—
833C22×D4—21no—
834C22×D4—21no—
835C22×D4—21no—
836C22×D4C23×C3711yescharacteristic
837C22×D4C23×C3711yescharacteristic
838C22×D4C23×C3712yes—
839C23×C4—21no—
840C23×C4—21no—
841AGL(1,ℤ/8)—44no—
842#135—44no—
843C2×Q16C23×C3712yes—
844C2×SD16C23×C3712yes—
845C2×SD16C23×C3712yes—
846C2×SD16C23×C3712yes—
847C2×SD16C23×C3712yes—
848C2×SD16C23×C3712yes—
849C2×D8—44no—
850C2×D8C23×C3712yes—
851C2×D8C23×C3712yes—
852C2×D8C23×C3712yes—
853C2×D8C23×C3712yes—
854C2×D8C23×C3712yes—
855C2×D8C23×C3712yes—
856C2×M16C23×C3712yes—
857C22×C8C23×C3712yes—
858C22×C8C23×C3712yes—
859C4⋊Q8C23×C3711yescharacteristic
860C4⋊Q8C23×C3711yescharacteristic
861C4⋊Q8C23×C3711yescharacteristic
862#127—22no—
863#127—21no—
864#127—21no—
865#127C23×C3711yescharacteristic
866#127C23×C3711yescharacteristic
867#127C23×C3712yes—
868#127C23×C3711yescharacteristic
869#126—21no—
870#126—21no—
871#126—21no—
872#126—21no—
873#125—21no—
874#125—21no—
875#125C23×C3711yescharacteristic
876#125C23×C3711yescharacteristic
877#124—21no—
878#124—22no—
879#124—21no—
880#124—21no—
881#124—21no—
882#124C23×C3711yescharacteristic
883#124C23×C3711yescharacteristic
884#124C23×C3712yes—
885#124C23×C3712yes—
886#123—21no—
887#123—21no—
888#123—21no—
889#123—21no—
890#123—21no—
891#123—21no—
892#123—22no—
893#123—22no—
894#123—22no—
895#123—22no—
896#123—21no—
897#123—21no—
898C22⋊Q8—21no—
899C22⋊Q8—21no—
900C22⋊Q8—21no—
901C22⋊Q8—21no—
902C22⋊Q8—21no—
903C22⋊Q8—21no—
904C22⋊Q8C23×C3711yescharacteristic
905C22⋊Q8C23×C3711yescharacteristic
906C22⋊Q8C23×C3712yes—
907#121—21no—
908#121—21no—
909#121—21no—
910#121—21no—
911#121—21no—
912#121—21no—
913#121—21no—
914#121—21no—
915#121—21no—
916#121—21no—
917#121—21no—
918#121—21no—
919#121—22no—
920#121—22no—
921#121—22no—
922#121—22no—
923#121C23×C3711yescharacteristic
924#121C23×C3711yescharacteristic
925#121C23×C3712yes—
926#121C23×C3711yescharacteristic
927#121C23×C3712yes—
928#121C23×C3711yescharacteristic
929#120—21no—
930#120—21no—
931#120—22no—
932#120—22no—
933#120—21no—
934#120—21no—
935C4×Q8—21no—
936C4×Q8D4×C3711yescharacteristic
937C4×Q8C23×C3711yescharacteristic
938C4×Q8C23×C3711yescharacteristic
939C4×Q8C23×C3712yes—
940C4×Q8C23×C3711yescharacteristic
941C4×D4—21no—
942C4×D4—21no—
943C4×D4—21no—
944C4×D4—21no—
945C4×D4—21no—
946C4×D4—21no—
947C4×D4—22no—
948C4×D4—22no—
949C4×D4—21no—
950C4×D4—21no—
951C4×D4—21no—
952C4×D4—21no—
953C4×D4—21no—
954C4×D4—21no—
955C4×D4—21no—
956C4×D4—21no—
957C4×D4—21no—
958C4×D4—21no—
959C4×D4—21no—
960C4×D4—21no—
961C4×D4—21no—
962C4×D4D4×C3711yescharacteristic
963C4×D4D4×C3711yescharacteristic
964C4×D4D4×C3711yescharacteristic
965C4×D4C23×C3711yescharacteristic
966C4×D4C23×C3711yescharacteristic
967C4×D4C23×C3711yescharacteristic
968C4×D4C23×C3711yescharacteristic
969C4×D4C23×C3711yescharacteristic
970C4×D4C23×C3711yescharacteristic
971C4×D4C23×C3711yescharacteristic
972C4×D4C23×C3711yescharacteristic
973C4×D4C23×C3712yes—
974C4×D4C23×C3712yes—
975C4×D4C23×C3711yescharacteristic
976C4×D4C23×C3711yescharacteristic
977C4×D4C23×C3711yescharacteristic
978#117—21no—
979#117—21no—
980#117—21no—
981#117—21no—
982#117D4×C3711yescharacteristic
983#117D4×C3711yescharacteristic
984#117D4×C3711yescharacteristic
985#117C23×C3711yescharacteristic
986C2×C4⋊C4—21no—
987C2×C4⋊C4C23×C3711yescharacteristic
988C2×C4⋊C4C23×C3711yescharacteristic
989C2×C22⋊C4—21no—
990C2×C22⋊C4—21no—
991C2×C22⋊C4—21no—
992C2×C22⋊C4—21no—
993C2×C22⋊C4—22no—
994C2×C22⋊C4—22no—
995C2×C42—21no—
996C2×C42C23×C3711yescharacteristic
997C2×C42C23×C3711yescharacteristic
998C2×C42C23×C3711yescharacteristic
999#107C23×C3712yes—
1000#107C23×C3712yes—
1001#107C23×C3712yes—
1002#106C23×C3712yes—
1003C4⋊C8C23×C3711yescharacteristic
1004C4⋊C8C23×C3711yescharacteristic
1005C4⋊C8C23×C3711yescharacteristic
1006C4⋊C8C23×C3712yes—
1007C4⋊C8C23×C3712yes—
1008C4⋊C8C23×C3712yes—
1009C4⋊C8C23×C3711yescharacteristic
1010#103C23×C3712yes—
1011#103C23×C3712yes—
1012#103C23×C3712yes—
1013#103C23×C3712yes—
1014#103C23×C3712yes—
1015#102C23×C3712yes—
1016#102C23×C3712yes—
1017#102C23×C3712yes—
1018#102C23×C3712yes—
1019#102C23×C3712yes—
1020#102C23×C3712yes—
1021#102C23×C3712yes—
1022#102C23×C3712yes—
1023#102C23×C3712yes—
1024#102C23×C3712yes—
1025#102C23×C3712yes—
1026C22⋊C8C23×C3712yes—
1027C22⋊C8C23×C3712yes—
1028C22⋊C8C23×C3712yes—
1029#97C23×C3712yes—
1030#97C23×C3712yes—
1031C4×C8C23×C3712yes—
1032C24—21no—
1033C24—21no—
1034C24—22no—
1035#41—22no—
1036#41—42no—
1037#41—41no—
1038#41—42no—
1039#41—42no—
1040#41—42no—
1041#41—42no—
1042#41—82no—
1043#41—82no—
1044#41—82no—
1045C2×Q8—21no—
1046C2×Q8—21no—
1047C2×Q8C2×D4×C3711yescharacteristic
1048C2×Q8C24×C3712yes—
1049C2×Q8C24×C3711yescharacteristic
1050C2×D4—22no—
1051C2×D4—22no—
1052C2×D4—21no—
1053C2×D4—21no—
1054C2×D4—21no—
1055C2×D4—22no—
1056C2×D4—22no—
1057C2×D4—21no—
1058C2×D4—21no—
1059C2×D4—22no—
1060C2×D4—22no—
1061C2×D4—21no—
1062C2×D4—21no—
1063C2×D4—21no—
1064C2×D4—21no—
1065C2×D4—21no—
1066C2×D4—22no—
1067C2×D4—21no—
1068C2×D4—21no—
1069C2×D4—21no—
1070C2×D4—22no—
1071C2×D4—22no—
1072C2×D4—41no—
1073C2×D4—41no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—82no—
1079C2×D4C2×D4×C3711yescharacteristic
1080C2×D4C2×D4×C3711yescharacteristic
1081C2×D4C2×D4×C3711yescharacteristic
1082C2×D4C24×C3712yes—
1083C2×D4C24×C3712yes—
1084C2×D4C24×C3711yescharacteristic
1085C2×D4C24×C3711yescharacteristic
1086C2×D4C24×C3711yescharacteristic
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—82no—
1103C22×C4—82no—
1104C22×C4C2×D4×C3711yescharacteristic
1105C22×C4C2×D4×C3711yescharacteristic
1106C22×C4C2×D4×C3711yescharacteristic
1107C22×C4C2×D4×C3711yescharacteristic
1108C22×C4C2×D4×C3711yescharacteristic
1109C22×C4C2×D4×C3711yescharacteristic
1110C22×C4C24×C3711yescharacteristic
1111C22×C4C24×C3711yescharacteristic
1112C22×C4C24×C3711yescharacteristic
1113Q16—42no—
1114SD16—24no—
1115SD16—42no—
1116SD16—42no—
1117SD16—42no—
1118SD16—42no—
1119D8—24no—
1120D8—24no—
1121D8—42no—
1122D8—42no—
1123D8—42no—
1124D8—42no—
1125M16—42no—
1126C2×C8—42no—
1127C2×C8—42no—
1128C2×C8C24×C3712yes—
1129C2×C8C24×C3712yes—
1130C2×C8C24×C3712yes—
1131C2×C8C24×C3712yes—
1132C4⋊C4—21no—
1133C4⋊C4—21no—
1134C4⋊C4—21no—
1135C4⋊C4—21no—
1136C4⋊C4—21no—
1137C4⋊C4—21no—
1138C4⋊C4—21no—
1139C4⋊C4—21no—
1140C4⋊C4—21no—
1141C4⋊C4—21no—
1142C4⋊C4—21no—
1143C4⋊C4—21no—
1144C4⋊C4—21no—
1145C4⋊C4—21no—
1146C4⋊C4—22no—
1147C4⋊C4—22no—
1148C4⋊C4C2×D4×C3711yescharacteristic
1149C4⋊C4C2×D4×C3711yescharacteristic
1150C4⋊C4C2×D4×C3711yescharacteristic
1151C4⋊C4C2×D4×C3711yescharacteristic
1152C4⋊C4C2×D4×C3711yescharacteristic
1153C4⋊C4C2×D4×C3711yescharacteristic
1154C4⋊C4C24×C3711yescharacteristic
1155C4⋊C4C24×C3711yescharacteristic
1156C4⋊C4C24×C3711yescharacteristic
1157C4⋊C4C24×C3711yescharacteristic
1158C4⋊C4C24×C3712yes—
1159C22⋊C4—22no—
1160C22⋊C4—21no—
1161C22⋊C4—21no—
1162C22⋊C4—21no—
1163C22⋊C4—21no—
1164C22⋊C4—22no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—22no—
1168C22⋊C4—21no—
1169C22⋊C4—21no—
1170C22⋊C4—21no—
1171C22⋊C4—21no—
1172C22⋊C4—21no—
1173C22⋊C4—21no—
1174C22⋊C4—21no—
1175C22⋊C4—21no—
1176C22⋊C4—21no—
1177C22⋊C4—21no—
1178C22⋊C4—21no—
1179C22⋊C4—21no—
1180C22⋊C4—21no—
1181C22⋊C4—21no—
1182C22⋊C4—21no—
1183C22⋊C4—22no—
1184C22⋊C4—22no—
1185C22⋊C4—22no—
1186C22⋊C4—22no—
1187C22⋊C4C2×D4×C3711yescharacteristic
1188C22⋊C4C2×D4×C3711yescharacteristic
1189C22⋊C4C2×D4×C3711yescharacteristic
1190C22⋊C4C2×D4×C3711yescharacteristic
1191C22⋊C4C2×D4×C3711yescharacteristic
1192C22⋊C4C2×D4×C3711yescharacteristic
1193C42—21no—
1194C42—21no—
1195C42—21no—
1196C42—22no—
1197C42C2×D4×C3711yescharacteristic
1198C42C2×D4×C3711yescharacteristic
1199C42C2×D4×C3711yescharacteristic
1200C42C2×D4×C3711yescharacteristic
1201C42C2×D4×C3711yescharacteristic
1202C42C2×D4×C3711yescharacteristic
1203C42C24×C3711yescharacteristic
1204C42C24×C3711yescharacteristic
1205C42C24×C3711yescharacteristic
1206C42C24×C3711yescharacteristic
1207C23—21no—
1208C23—21no—
1209C23—21no—
1210C23—22no—
1211C23—22no—
1212C23—42no—
1213C23—42no—
1214C23—42no—
1215C23—42no—
1216C23—44no—
1217C23—81no—
1218C23—81no—
1219C23—82no—
1220C23—82no—
1221C23C22×D4×C3711yescharacteristic
1222C23C22×D4×C3711yescharacteristic
1223C23C22×D4×C3711yescharacteristic
1224Q8—22no—
1225Q8—21no—
1226Q8—21no—
1227Q8—22no—
1228Q8—41no—
1229Q8—42no—
1230Q8—81no—
1231D4—22no—
1232D4—22no—
1233D4—22no—
1234D4—22no—
1235D4—21no—
1236D4—21no—
1237D4—21no—
1238D4—21no—
1239D4—22no—
1240D4—21no—
1241D4—22no—
1242D4—41no—
1243D4—42no—
1244D4—42no—
1245D4—42no—
1246D4—42no—
1247D4—44no—
1248D4—42no—
1249D4—42no—
1250D4—42no—
1251D4—42no—
1252D4—42no—
1253D4—42no—
1254D4—82no—
1255D4—82no—
1256D4—81no—
1257D4—82no—
1258D4—82no—
1259D4—81no—
1260D4—81no—
1261D4—82no—
1262D4—82no—
1263D4H(5,𝔽2)×C3712yes—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—81no—
1289C2×C4—81no—
1290C2×C4—81no—
1291C2×C4—81no—
1292C2×C4—82no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4—81no—
1297C2×C4—81no—
1298C2×C4C22×D4×C3711yescharacteristic
1299C2×C4C22×D4×C3711yescharacteristic
1300C2×C4C22×D4×C3711yescharacteristic
1301C2×C4C22×D4×C3711yescharacteristic
1302C2×C4C22×D4×C3711yescharacteristic
1303C2×C4C22×D4×C3711yescharacteristic
1304C2×C4C22×D4×C3711yescharacteristic
1305C2×C4C22×D4×C3711yescharacteristic
1306C2×C4C22×D4×C3711yescharacteristic
1307C2×C4C22×D4×C3711yescharacteristic
1308C2×C4C22×D4×C3711yescharacteristic
1309C2×C4C25×C3711yescharacteristic
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C8—22no—
1314C22—21no—
1315C22—21no—
1316C22—21no—
1317C22—21no—
1318C22—22no—
1319C22—21no—
1320C22—21no—
1321C22—21no—
1322C22—21no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—42no—
1332C22—42no—
1333C22—41no—
1334C22—41no—
1335C22—42no—
1336C22—42no—
1337C22—84no—
1338C22—84no—
1339C22—164no—
1340C22C37×#57512yes—
1341C22C23×D4×C3711yescharacteristic
1342C4—21no—
1343C4—21no—
1344C4—21no—
1345C4—21no—
1346C4—21no—
1347C4—21no—
1348C4—21no—
1349C4—21no—
1350C4—21no—
1351C4—21no—
1352C4—41no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4C37×#57612yes—
1360C4C2×H(5,𝔽2)×C3711yescharacteristic
1361C4C37×#58511yescharacteristic
1362C2—22no—
1363C2—41no—
1364C2—41no—
1365C2—42no—
1366C2—81no—
1367C2—81no—
1368C2—82no—
1369C2—82no—
1370C2C37×#348811yescharacteristic
1371C2C2×C37×#57511yescharacteristic
1372C2C2×C37×#57611yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C4×#41×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C37×#3508C2semidirect
2. C37×#3481C2semidirect
3. C37×#3403C2semidirect
4. C37×#3370C2semidirect
5. C37×#3314C2semidirect
6. C37×#3309C2semidirect
7. C37×#3297C2semidirect
8. C37×#3280C2semidirect
9. C37×#3268C2semidirect
10. C37×#3264C2semidirect
11. C37×#3251C2semidirect
12. C37×#3248C2semidirect
13. C37×#3245C2semidirect
14. C37×#3217C2semidirect
15. C37×#3214C2semidirect
16. C37×#3212C2semidirect
17. C37×#3115C2semidirect
18. C37×#3110C2semidirect
19. C37×#3100C2semidirect
20. C37×#3036C2semidirect
21. C37×#3035C2semidirect
22. C2×C37×#459C2semidirect
23. C37×#2990C2semidirect
24. C2×AGL(1,ℤ/8)×C37C22semidirect
25. C2×#135×C37C22semidirect
28. C37×#559C22semidirect
29. C37×#559C22semidirect
31. C37×#554C22semidirect
34. C37×#553C22semidirect
38. C37×#550C22semidirect
44. C37×#546C22semidirect
45. C37×#546C22semidirect
50. C37×#533C22semidirect
51. C37×#532C22semidirect
52. C37×#532C22semidirect
53. C37×#532C22semidirect
54. C37×#532C22semidirect
55. C37×#532C22semidirect
56. C2×#127×C37C22semidirect
59. C37×#529C22semidirect
64. C4×#41×C37C22semidirect
67. C2×C4×D4×C37C22semidirect
68. C37×#496C22semidirect
69. C37×#496C22semidirect
70. C37×#495C22semidirect
71. C37×#490C22semidirect
72. C37×#489C22semidirect
73. C37×#488C22semidirect
74. C37×#484C22semidirect
75. C37×#482C22semidirect
76. C37×#480C22semidirect
77. C37×#479C22semidirect
78. C37×#478C22semidirect
79. C37×#475C22semidirect
80. C37×#474C22semidirect
81. C37×#474C22semidirect
82. C37×#474C22semidirect
83. C37×#474C22semidirect
84. C37×#469C22semidirect
85. C37×#468C22semidirect
86. C37×#467C22semidirect
87. C37×#466C22semidirect
88. C37×#466C22semidirect
90. C37×#464C22semidirect
91. C37×#464C22semidirect
92. C37×#463C22semidirect
93. C37×#463C22semidirect
94. C37×#463C22semidirect
95. C37×#463C22semidirect
96. C37×#462C22semidirect
97. C37×#461C22semidirect
98. C37×#461C22semidirect
99. C37×#461C22semidirect
100. C37×#460C22semidirect
101. C37×#460C22semidirect
105. C37×#459C22semidirect
106. C37×#459C22semidirect
107. C37×#459C22semidirect
108. C37×#459C22semidirect
109. C37×#459C22semidirect
110. C37×#459C22semidirect
111. C37×#452C22semidirect
113. C37×#450C22semidirect
114. C37×#449C22semidirect
115. C37×#449C22semidirect
116. C37×#449C22semidirect
117. C37×#449C22semidirect
119. C37×#447C22semidirect
120. C37×#446C22semidirect
121. C37×#442C22semidirect
122. C37×#440C22semidirect
123. C37×#440C22semidirect
124. C37×#440C22semidirect
125. C4×D8×C37C22semidirect
126. C4×D8×C37C22semidirect
128. C37×#435C22semidirect
129. C8×D4×C37C22semidirect
130. C37×#432C22semidirect
131. C37×#432C22semidirect
132. C37×#431C22semidirect
133. C37×#423C22semidirect
134. C2×C4⋊C8×C37C22semidirect
135. C2×C4⋊C8×C37C22semidirect
136. C37×#417C22semidirect
137. C37×#416C22semidirect
138. C2×#102×C37C22semidirect
627. #61977C37direct (N × H)
676. #3508C2×C37semidirect
677. #3481C2×C37semidirect
678. #3403C2×C37semidirect
679. #3370C2×C37semidirect
680. #3314C2×C37semidirect
681. #3309C2×C37semidirect
682. #3297C2×C37semidirect
683. #3280C2×C37semidirect
684. #3268C2×C37semidirect
685. #3264C2×C37semidirect
686. #3251C2×C37semidirect
687. #3248C2×C37semidirect
688. #3245C2×C37semidirect
689. #3217C2×C37semidirect
690. #3214C2×C37semidirect
691. #3212C2×C37semidirect
692. #3115C2×C37semidirect
693. #3110C2×C37semidirect
694. #3100C2×C37semidirect
695. #3036C2×C37semidirect
696. #3035C2×C37semidirect
697. C2×#459C2×C37semidirect
698. #2990C2×C37semidirect
710. C2×AGL(1,ℤ/8)C22×C37semidirect
711. C2×#135C22×C37semidirect
714. #559C22×C37semidirect
715. #559C22×C37semidirect
717. #554C22×C37semidirect
720. #553C22×C37semidirect
724. #550C22×C37semidirect
730. #546C22×C37semidirect
731. #546C22×C37semidirect
736. #533C22×C37semidirect
737. #532C22×C37semidirect
738. #532C22×C37semidirect
739. #532C22×C37semidirect
740. #532C22×C37semidirect
741. #532C22×C37semidirect
742. C2×#127C22×C37semidirect
745. #529C22×C37semidirect
750. C4×#41C22×C37semidirect
753. C2×C4×D4C22×C37semidirect
754. #496C22×C37semidirect
755. #496C22×C37semidirect
756. #495C22×C37semidirect
757. #490C22×C37semidirect
758. #489C22×C37semidirect
759. #488C22×C37semidirect
760. #484C22×C37semidirect
761. #482C22×C37semidirect
762. #480C22×C37semidirect
763. #479C22×C37semidirect
764. #478C22×C37semidirect
765. #475C22×C37semidirect
766. #474C22×C37semidirect
767. #474C22×C37semidirect
768. #474C22×C37semidirect
769. #474C22×C37semidirect
770. #469C22×C37semidirect
771. #468C22×C37semidirect
772. #467C22×C37semidirect
773. #466C22×C37semidirect
774. #466C22×C37semidirect
776. #464C22×C37semidirect
777. #464C22×C37semidirect
778. #463C22×C37semidirect
779. #463C22×C37semidirect
780. #463C22×C37semidirect
781. #463C22×C37semidirect
782. #462C22×C37semidirect
783. #461C22×C37semidirect
784. #461C22×C37semidirect
785. #461C22×C37semidirect
786. #460C22×C37semidirect
787. #460C22×C37semidirect
791. #459C22×C37semidirect
792. #459C22×C37semidirect
793. #459C22×C37semidirect
794. #459C22×C37semidirect
795. #459C22×C37semidirect
796. #459C22×C37semidirect
797. #452C22×C37semidirect
799. #450C22×C37semidirect
800. #449C22×C37semidirect
801. #449C22×C37semidirect
802. #449C22×C37semidirect
803. #449C22×C37semidirect
805. #447C22×C37semidirect
806. #446C22×C37semidirect
807. #442C22×C37semidirect
808. #440C22×C37semidirect
809. #440C22×C37semidirect
810. #440C22×C37semidirect
811. C4×D8C22×C37semidirect
812. C4×D8C22×C37semidirect
814. #435C22×C37semidirect
815. C8×D4C22×C37semidirect
816. #432C22×C37semidirect
817. #432C22×C37semidirect
818. #431C22×C37semidirect
819. #423C22×C37semidirect
820. C2×C4⋊C8C22×C37semidirect
821. C2×C4⋊C8C22×C37semidirect
822. #417C22×C37semidirect
823. #416C22×C37semidirect
824. C2×#102C22×C37semidirect
825. C37#61977direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C37×#35082
C37×#34812
C37×#34032
C37×#33702
C37×#33142
C37×#33092
C37×#32972
C37×#32802
C37×#32682
C37×#32642
C37×#32512
C37×#32482
C37×#32452
C37×#32172
C37×#32142
C37×#32122
C37×#31152
C37×#31102
C37×#31002
C37×#30362
C37×#30352
C2×C37×#4592
C37×#29902
#6197737